Chapter 5, Section 4
Multiplying polynomials
With monomials, simply associate like factors and simplify by combining like terms.
 1 2  x 
4
  x   (6 x )
2
3



With a monomial times a polynomial, distribute and simplify by combining like terms.
 a 3 a 2b

3ab 
 ab 2  2b 3 
6
 3

(a  b)(a 4  2a 3 b  a 2 b  b 3 )
In the special case when there’s a binomial times a binomial – which happens a lot –
there’s a special method called “FOIL” that helps you remember to distribute and then
you simplify by combining like terms.
FOIL stands for First, Outer, Inner, Last
With (a + b)(x + y)
a and x are First
a and y are Outer
b and x are Inner
b and y are Last
In this case there are no like terms when you’re done multiplying you get:
ax + ay + bx + by.
Look at (x + 2) ( x  y)
First
Outer
Inner
Last
Combine like terms to get _______________________________________________
If you have three binomial factors you simply use foil on any two and then distribute the
third over the result.
( x  y)( 2x + y) (x  1)
First
Outer
Inner
Last
Combine like terms to get
Distribute the remaining term over the polynomial, combine like terms.
There’s a ton of practice in your book and on the Worksheet A.
Let’s do two more
A.
(2x  3) ( x + 3)
First
Outer
Inner
Last
Combine like terms to get
__________________________________________________________________
B.
( 5x 2) ( x + 3)
First
Outer
Inner
Last
Combine like terms to get
__________________________________________________________________